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- Thread starter jdavel
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Gib Z

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For your specific integral, There are a few ways of doing it.

A common way is (writing 1/cos x as sec x) multiplying the integrand through by (sec x + tan x). However, that makes it seem like you've already done this before and hence you know you can rely of this otherwise remarkable step.

So the way I prefer to do it as many people might see more easily, though it takes some more work. Multiply the integrand through by cos x, use the pythagorean identity on the denominator, a simple substitution and partial fractions, were home free =]

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Very nice!

Let me ask you something. If you were teaching integration, how would you explain to your students what went through your head to come up with the idea of multiplying the integrand by cos(x)/cos(x)? Is there an insight that could be used when they hit another integral that doesn't seem to have an obvious method of solution? Did you see all at once the whole "....cos squared of x in the denominaor is going to give me a function of sin(x) through the Pythagorean theorem, and the differential for that will have cos(x) in it, which is just what I'll need for the cos(x)dx that I've created in the numerator...." ?

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Gib Z

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